62 



TESTING TECHNIQUE 



The reciprocity method is based on the fact that for 

 a passive linear electroaconstic transducer which 

 obeys the reciprocity principle (this includes most 

 transducers now in use), a definite and simple rela- 

 tionship holds between its response as a transmitter 

 and as a receiver. Consider an electroacoustic trans- 

 ducer with its acoustic center (which may be arbitrar- 

 ily selected) located at a point P„. The transducer is 

 being operated as a transmitter with a current / flow- 

 ing into it. At some other arbitrary point P the trans- 

 ducer produces a pressure p. Let S be the transmitting 

 sensitivity expressed as the ratio of the pressure at P 

 to the current / (that is, S = pjl). Suppose that there 

 is placed at the pointP the center of a source of spheri- 

 cal waves, and let p,. be the pressure produced at the 

 point P when the transducer is not present. If the 

 transducer is present, it develops in this sound field 

 an open-circuit voltage E across its terminals. Let 

 the ratio of E to p c be the receiving sensitivity M 

 (M = E/p c ). The reciprocity principle then states that 



M 



S 



2d\ 

 pc 



(56) 



where d is the distance from P to P„, A is the wave 

 length, and p and c are respectively the density and 

 sound velocity of the medium in which the trans- 

 ducer is present. 



To make use of the reciprocity principle for the ab- 

 solute calibration of a transducer, three transducers 

 are employed. One is used only as a transmitter or 

 projector, a second only as a receiver, while the third 

 must be a reversible transducer obeying the reciproc- 

 ity principle. The projector is placed at a point P 

 with a definite orientation. The receiver is placed at 

 a point P' sufficiently distant from P so that the waves 

 reaching it from the projector are essentially plane. 

 Then for a given current /,, in the projector, the volt- 

 age developed by the receiver is measured, either on 

 open-circuit or across an impedance kept constant 

 during the measurements. This voltage is denoted by 

 E IlP . The receiver is now replaced by the transducer 

 and the open-circuit voltage developed by it, E TP , is 

 measured for the same current /,, in the projector. 

 Next, the projector is replaced by the receiver, whose 

 orientation with respect to the transducer must be the 

 same as it was previously with respect to the projector. 

 The transducer is then operated as a transmitter with 

 a current I T , and the voltage developed by the re- 

 ceiver E RT is obtained. 



If M R denotes the sensitivity of the receiver and M T 

 the open-circuit receiving sensitivity of the trans- 

 ducer, then, since the pressure developed by the pro- 

 jector is the same in the first two trials, 



Mr _ E h 

 M T Ej 



(57) 



If .S' r is the transmitting sensitivity of the trans- 

 ducer, that is, the ratio of the pressure produced at 

 the receiver to the current I T in the transducer, then 



(58) 



since S T I T is the pressure at the receiver. From the 

 reciprocity principle 



M T 



2dX 

 pc 



(59) 



where d is the distance from P to P'. Substituting the 

 value of S T from equation (59) in (58), 



F-rt — M n M T L 



(P£) 

 '2dX' 



(60) 



Eliminating M T between equations (60) and (57), 



F _ M (M n E TP ) . (pc) 



h «T- M " E RP ' T 2d\ (bl) 



Mr = |"|*£ . % . MT (62) 



\_E Tp J T PC J 



In this way, the calibration of the hydrophone H is 

 expressed in terms of measured quantities. The pre- 

 ceding discussion assumes cgs units for all quantities 

 thus including absolute electrical units. If volts and 

 amperes are used in equation (62), E RT must be mul- 

 tiplied by 10". Thus, the absolute calibration may 

 be obtained by a process which involves only elec- 

 trical measurements on the transducers. 



5.5.7 Notes on the Reciprocity Method 



To obviate any misunderstanding concerning the 

 use of the reciprocity method of calibration, the fol- 

 lowing notes are added: 



1 . The open-circuit voltage developed by the trans- 

 ducer T operating as a receiver should be measured 



